In an image displaying device represented by a rear projection type projection television, a screen is used, and image light emitted from an image light source is projected on the screen. In general, the screen of the image displaying device is formed by combining a lenticular and a Fresnel lens. The lenticular functions as a light diffusion plate in which the image light is scattered to form an image. In the Fresnel lens, the image light emitted from the image light source is refracted, and rays of refracted light go out to the lenticular almost in parallel to each other.
FIG. 1 is a view showing an external appearance of a conventional Fresnel lens.
In FIG. 1, 101 indicates a Fresnel lens seen on a slant. 102 indicates a sectional shape of the Fresnel lens 101. 103 indicates an optical axis of the Fresnel lens 101. 104 indicates a prism portion formed for each pitch area corresponding to one pitch length in the Fresnel lens 101.
In the manufacturing of the Fresnel lens 101, a metal mold (or a lens forming mold) is formed by rotating the mold on the optical axis 103, synthetic resin is poured into the metal mold, the synthetic resin is hardened, the metal mold is taken off from the synthetic resin, and the manufacturing of the Fresnel lens 101 is completed. On a surface of the manufactured Fresnel lens 101, a plurality of ring bands are formed in a concentric circular shape around the optical axis 103. As is realized by looking at the sectional shape 102 of the Fresnel lens 101, the ring bands formed in a concentric circular shape denote the plurality of prism portions 104.
That is, the prism portions 104 of the sectional shape 102 formed in a saw-tooth shape are equally spaced at pitch intervals respectively corresponding to one pitch width. One pitch width of the Fresnel lens 101 actually used is almost equal to 0.1 mm, and the pitch width is very small even though the pitch width is compared with each of minimum pixels on which an image is projected through the Fresnel lens 101.
The whole Fresnel lens 101 functions as one convex lens. Because the prism portions 104 can be thinned, rays of light incident on the Fresnel lens 101 can be changed or refracted almost without requiring a distance between an incident point of the ray of incident light and an outgoing point of a ray of outgoing light.
In the image displaying device, to shorten the depth of the image displaying device, image light is often injected on the Fresnel lens 101 of the screen from a direction inclined with respect to an incident normal of the Fresnel lens 101 as much as possible. Therefore, a thinned type image displaying device can be obtained.
FIG. 2 is a view showing the configuration of an image displaying device in which a conventional Fresnel lens is applied to a screen. A plurality of arrows indicate a plurality of rays of light.
111 indicates a light emitting source (or illumination light source means) for emitting a plurality of rays of light. 112 indicates a parabolic mirror (or illumination light source means). The light emitting source 111 is disposed on a focal point of the parabolic mirror 112. 113 indicates a converging lens (or converging optics means) for converging a plurality of rays of light reflected on the parabolic mirror 112. 114 indicates a light bulb (or optical modulating means) formed of liquid crystal. An intensity of each ray of light converged by the converging lens 113 is spatially changed in the light bulb 114 to modulate the converged rays of light according to display contents written on the light bulb 114.
115 indicates a projection optics lens (or projection optics means) for forming an image from the rays of light of which the intensities are changed by the light bulb 114. 116 indicates a rear projection type screen for receiving the image of the rays of light formed by the projection optics lens 115 from the rear side and displaying the image. The rays of light spreading in the projection optics lens 115 are changed in the screen 116 to a plurality of rays of light parallel to each other, the image formed from the rays of light is displayed on the screen 116, and the rays of light are diffused from the screen 116 to a wide area. Therefore, the screen 116 has a function for widening a view field.
In the screen 116, 117 indicates a Fresnel lens described before, and 118 indicates a lenticular.
In the Fresnel lens 117, the spreading rays of light sent from the projection optics lens 115 are received on an incident plane 117A, and the rays of light go out at a prescribed outgoing angle through a prism portion 117B arranged for each pitch area corresponding one pitch. In short, the Fresnel lens 117 is used to almost collimate the rays of light spreading in the projection optics lens 115. An image is formed on the lenticular 118 from the rays of light going out from the Fresnel lens 117, and the rays of light are diffused.
119 indicates an optical axis. The optical axis 119 exists for the parabolic mirror 112, the converging lens 113, the light bulb 114, the projection optics lens 115, the Fresnel lens 117 and the lenticular 118, and the optical axis 119 is perpendicular to the incident plane 117A of the Fresnel lens 117.
Next, an operation will be described below.
The light emitting source 111 disposed on a focal point of the parabolic mirror 112 can be almost regarded as a point source. Therefore, rays of light emitted from the light emitting source 111 are reflected on the parabolic mirror 112 and goes out to the converging lens 113 as almost parallel rays of light. When the parallel rays of light are converged by the converging lens 113 onto the light bulb 114, intensities of the converged rays of light are spatially changed by the light bulb 114 to modulate the converged rays of light according to display contents of the light bulb 114.
The rays of light intensity-modulated are projected on the rear surface of the screen 116 at a wide angle by the projection optics lens 115, and an image is formed from the rays of projected light. An angle between each ray of light and the optical axis 119 is called a projection angle. As shown in FIG. 2, the projection angle in each pitch area differs from those in the other pitch areas. However, because the pitch between each pair of prism portions 117B is considerably shorter than the lengths of the projection optics lens 115 and the screen 116, a plurality of rays of light incident on each prism portion 117B can be almost regarded as a plurality of parallel rays.
An angle between a normal m11 of the incident plane 117A and each ray of incident light denotes an incident angle. Because the incident angle of each ray of incident light is equal to the projection angle of the ray of incident light according to the relationship of alternate-interior angles obtained from a straight line (the incident ray) intersecting two parallel lines (the optical axis 119 and the normal m11), the more a pitch area receiving a ray of light approaches the optical axis 119, the smaller the incident angle of the ray of light is. Also, the more a pitch area receiving a ray of light is far away from the optical axis 119, the larger the incident angle of the ray of light is. In particular, the ray of light going out to the prism portion 117B placed at each end of the screen 116 is incident on the incident plane 117A at the maximum incident angle.
A size of the screen 116 is determined according to this maximum incident angle, or the maximum projection angle of the projection optics lens 115, and a projection distance from the projection optics lens 115 to the screen 116. In contrast, in a case where the size of the screen 116 is predetermined, the larger the maximum projection angle is, the more the projection distance can be shortened. Therefore, an optical system having a shortened distance in the direction of the optical axis 119 can be obtained, and the image displaying device can be thinned.
In the Fresnel lens 117, a plurality of rays of light are received on the incident plane 117A at the incident angles respectively, and the ray of light goes out to the lenticular 118 at a prescribed outgoing angle through the prism portion 117B arranged for each pitch area. The outgoing angle is defined as an angle between a straight line parallel to the optical axis 119 on the Fresnel lens 117 and the ray of light going out from the Fresnel lens 117. The outgoing angle is normally set to a small angle ranging from 0 degree to several degrees. In short, the rays of light going out from the Fresnel lens 117 are almost parallel to the optical axis 119 (the outgoing angle for the rays of light is set to 0 degree in FIG. 2). In this case, the higher the transmissivity (a ratio in power of the outgoing light to the incident light) of the Fresnel lens 117 for the rays of light, the better the Fresnel lens 117. Also, the higher the transmissivity, the more the image displayed on the screen 116 is bright.
In the lenticular 118, the rays of light are received from the prism portions 117B of the Fresnel lens 117. Also, though an image of the display contents of the light bulb 114 is formed by the projection optics lens 115, the rays of light indicating the image are diffused from the lenticular 118 in a direction (the right direction of the screen 116 in FIG. 2) directed toward a user. The user of the image displaying device views the rays of light diffused from each of a plurality of image forming points as an image. Because the rays of light are diffused by the lenticular 118, the user can view the image which has the brightness required in a certain view field.
As is described above, the larger the maximum projection angle of the projection optics lens 115, in other words, the larger the maximum incident angle of light to the Fresnel lens 117, the more the projection distance is shortened. Therefore, a thin type image displaying device having a shortened projection distance can be provided for the user.
In cases where a size of the screen 116 is predetermined by the specification of the screen 116, even though a large maximum projection angle is obtained by the function of the projection optics lens 115 or another optical unit, unless the Fresnel lens 117 receives a ray of light corresponding to the maximum projection angle, the projection distance cannot be shortened. In conclusion, it is an important point that the Fresnel lens 117 is designed so as to set the incident angle of a ray of light as large as possible on condition that the ray of light go out from the Fresnel lens 117 at high transmissivity.
Next, various principles of the conventional Fresnel lens will be described below.
FIG. 3A and FIG. 3B are respectively an enlarged view showing the sectional shape of a plurality of prism portions arranged in a plurality of pitch areas of the conventional Fresnel lens, FIG. 3A shows the sectional shape in case of a small incident angle, and FIG. 3B shows the sectional shape in case of a large incident angle. Each arrow in FIG. 3A and FIG. 3B indicates a ray of light.
In FIG. 3A and FIG. 3B, 121 indicates a Fresnel lens. 121A indicates a refraction type prism portion formed for each pitch area of the Fresnel lens 121.
121B indicates an incident plane of each refraction type prism portion 121A. The incident plane 121B is formed in a flat surface shape and is perpendicular to an optical axis (not shown) of the Fresnel lens 121. 121C indicates an outgoing plane of each refraction type prism portion 121A. 121Z indicates an ineffective plane of each refraction type prism portion 121A. Each refraction type prism portion 121A is shaped by the incident plane 121B, the outgoing plane 121C and the ineffective plane 121Z. Here, the ineffective plane 121Z does not participate with a ray of incident light or a ray of outgoing light.
Also, Li indicates a ray of light incident on the incident plane 121B. Lr indicates a ray of light reflected on the incident plane 121B. Lt indicates a ray of transmitted light refracted on the incident plane 121B and transmitted through the internal of the refraction type prism portion 121A. Lo indicates a ray of outgoing light refracted on the outgoing plane 121C and going out to the air. m12 indicates a normal of the incident plane 121B, and m13 indicates a normal of the outgoing plane 121C.
Next, an operation will be described below.
In FIG. 3A, when a ray of incident light Li transmitted through the air having a refractive index of unity comes on the Fresnel lens 121 having a refractive index of n (n>1) at a real incident angle “a” to the normal m14, the ray of incident light Li is divided on the incident plane 121B into a ray of transmitted light Lt transmitted at a refraction angle of χ and a ray of reflected light Lr transmitted at a reflection angle of “a”. The ray of reflected light Lr causes a loss to the Fresnel lens 121.
The ray of transmitted light Lt refracted on the incident plane 121B and transmitted through the internal of the refraction type prism portion 121A makes an angle of φ to the normal m13 and reaches the outgoing plane 121C. A part of the ray of transmitted light Lt is changed to a ray of reflected light (not shown), and the remaining part of the ray of transmitted light Lt crosses the outgoing plane 121C and goes out as a ray of outgoing light Lo at an outgoing angle of “f”.
As is described above, the ray of incident light Li incident on the Fresnel lens 121 at the incident angle of “a” makes a turn in the Fresnel lens 121 to a direction of an outgoing angle of “f”. Because the ray of incident light Li is received on the incident plane 121B formed in a flat surface shape, the Fresnel lens 121 has a special feature in that the ray of incident light Li is received in the Fresnel lens 121 at a high light-receiving efficiency.
In cases where the incident angle of a ray of incident light becomes smaller, the transmissivity of the incident plane is heightened, and the reflectivity of the incident plane is lowered. In contrast, in cases where the incident angle of a ray of light becomes larger, the transmissivity of the incident plane is lowered, and the reflectivity of the incident plane is heightened. This phenomenon is well-known as an optical theory. Accordingly, as shown in FIG. 3B, when the incident angle “a” of a ray of light becomes larger, a ratio of the ray of transmitted light Lt to the ray of incident light Li is decreased, and a ratio of the ray of reflected light Lr to the ray of incident light Li is increased. Therefore, the transmissivity of the Fresnel lens 121 is undesirably lowered.
In short, the transmissivity of the Fresnel lens 121 depends on the incident angle. The larger the incident angle “a”, the more the transmissivity is lowered. Also, in cases where the Fresnel lens 121 is applied to a screen of which the size is predetermined, the thinning of the image displaying device is undesirably restricted due to the limitation of the maximum incident angle.
In another type of Fresnel lens having the refraction type prism portion, as is described below, the structure on the incident side of the refraction type prism portion 121A shown in FIG. 3A and FIG. 3B is changed to that on an outgoing side, and the structure on the outgoing side of the refraction type prism portion 121A shown in FIG. 3A and FIG. 3B is changed to that on an incident side.
FIG. 4A and FIG. 4B are enlarged views respectively showing the sectional shape of a plurality of prism portions arranged in a plurality of pitch areas of another type conventional Fresnel lens, FIG. 4A shows the sectional shape in case of a small incident angle, and FIG. 4B shows the sectional shape in case of a large incident angle. An arrow in each of FIG. 4A and FIG. 4B indicates a ray of light.
In FIG. 4A and FIG. 4B, 131 indicates a Fresnel lens. 131A indicates a refraction type prism portion formed for each pitch area of the Fresnel lens 131.
131B indicates an incident plane of each refraction type prism portion 131A. 131C indicates an outgoing plane of each refraction type prism portion 131A. 131Z indicates an ineffective plane of each refraction type prism portion 131A. Each refraction type prism portion 131A is shaped by the incident plane 131B, the outgoing plane 131C and the ineffective plane 131Z. The incident plane 131B is formed in a flat surface shape and is perpendicular to an optical axis (not shown) of the Fresnel lens 131. Though rays of light are received on the ineffective plane 131Z, the ineffective plane 131Z does not participate in the going-out of a ray of light from the outgoing plane 131C.
Also, Li indicates a ray of light incident on the incident plane 131B. Lr indicates a ray of light reflected on the incident plane 131B. Lt indicates a ray of transmitted light refracted on the incident plane 131B and transmitted through the internal of the refraction type prism portion 131A. Lo indicates a ray of outgoing light refracted on the outgoing plane 131C and going out to the air. Le indicates a ray of ineffective light received on the ineffective plane 131Z. m14 indicates a normal of the outgoing plane 131C, and m15 indicates a normal of the incident plane 131B.
Next, an operation will be described below.
In FIG. 4A, when a ray of incident light Li transmitted through the air having a refractive index of unity comes on the Fresnel lens 131 having a refractive index of n (n>1) at an incident angle of “a” to the normal m14, the ray of incident light Li is incident on the incident plane 131B at a real incident angle of “b” to the normal m15, and the ray of incident light Li is divided on the incident plane 131B into a ray of transmitted light Lt transmitted at a refraction angle of χ and a ray of reflected light Lr transmitted at a reflection angle of “b”. The ray of reflected light Lr causes a loss to the Fresnel lens 131.
The ray of transmitted light Lt refracted on the incident plane 131B and transmitted through the refraction type prism portion 131A makes an angle of φ to the normal m14 and reaches the outgoing plane 131C. A part of the ray of transmitted light Lt is changed to a ray of reflected light (not shown), and the remaining part of the ray of transmitted light Lt crosses the outgoing plane 131C and goes out as a ray of outgoing light Lo at an outgoing angle of “f”.
Also, because the ray of ineffective light Le received on the ineffective plane 131Z goes out from the outgoing plane 131C at an angle different from the outgoing angle of “f”, the ray of ineffective light Le causes a loss to the Fresnel lens 131.
As is described above, the ray of incident light Li incident on the Fresnel lens 131 at the incident angle of “a” makes a turn in the Fresnel lens 131 to a direction of the outgoing angle of “f”. Because the Fresnel lens 131 has the outgoing plane 131C formed in a flat surface shape, in cases where the Fresnel lens 131 is applied to a screen, the Fresnel lens 131 has a special feature in that a lenticular can be integrally formed with the outgoing plane 131C.
However, for the same reason as that in the Fresnel lens 121, as shown in FIG. 4B, in cases where the incident angle of “a” becomes larger, a ratio of the ray of reflected light Lr to the ray of incident light Li is undesirably increased, and an area (an area of slash marks in each of FIG. 4A and FIG. 4B) of the ray of ineffective light received on the ineffective plane 131Z is undesirably enlarged.
Therefore, in the same manner as in the Fresnel lens 121, the transmissivity of the Fresnel lens 131 depends on the incident angle. And, the larger the incident angle, the more the transmissivity is lowered.
As is described above, in cases where the incident angle in the Fresnel lens 131 having the refraction type prism portions is increased, the transmissivity of the Fresnel lens 131 is undesirably lowered. Also, in cases where the Fresnel lens 131 is applied to a screen of which the size is predetermined, the thinning of the image displaying device is undesirably restricted due to the lowering of the transmissivity of the Fresnel lens 131.
To remedy the above-described defects in the conventional Fresnel lens having the refraction type prism portions and to obtain a high transmissivity of the Fresnel lens in case of a large incident angle, another conventional Fresnel lens will be described below.
FIG. 5A and FIG. 5B are enlarged views respectively showing the sectional shape of a plurality of prism portions arranged in a plurality of pitch areas of another type conventional Fresnel lens, FIG. 5A shows the sectional shape in case of a large incident angle, and FIG. 5B shows the sectional shape in case of a small incident angle. Each arrow in FIG. 5A and FIG. 5B indicates a ray of light.
In FIG. 5A and FIG. 5B, 141 indicates a Fresnel lens. 141A indicates a total reflection type prism portion formed for each pitch area of the Fresnel lens 141.
141B indicates an incident plane of each total reflection type prism portion 141A. 141C indicates a total reflection plane of each total reflection type prism portion 141A. 141D indicates an outgoing plane of each total reflection type prism portion 141A. Each total reflection type prism portion 141A is shaped by the incident plane 141B, the total reflection plane 141C and the outgoing plane 141D. The outgoing plane 141D is formed in a flat surface shape and is perpendicular to an optical axis (not shown) of the Fresnel lens 141. In a case where a ray of light transmitted through a high refractive index type medium is incident on a plane between the high refractive index type medium and a low refractive index type medium at a large incident angle larger than a critical angle, the ray of light is totally reflected on the plane. This phenomenon is used in the reflection performed on the total reflection plane 141C.
Also, Li indicates a ray of light incident on the incident plane 141B. Lt1 indicates a ray of transmitted light refracted on the incident plane 141B and transmitted through the total reflection plane 141C. Lt2 indicates a ray of transmitted light totally reflected on the total reflection plane 141C and transmitted to the outgoing plane 141D. Lo indicates a ray of outgoing light refracted on the outgoing plane 141D and going out to the air. Le indicates a ray of ineffective light received on the incident plane 141B. m16 indicates a normal of the outgoing plane 141D, m17 indicates a normal of the incident plane 141B, and m18 indicates a normal of the total reflection plane 141C.
Next, an operation will be described below.
In FIG. 5A, when a ray of incident light Li transmitted through the air having a refractive index of unity comes on the Fresnel lens 141 having a refractive index of n (n>1) at an incident angle of “a” to the normal m16, the ray of incident light Li is incident on the incident plane 141B at a real incident angle of “b” to the normal m17, and the ray of incident light Li is divided on the incident plane 141B into a ray of transmitted light Lt1 transmitted at a refraction angle of χ and a ray of reflected light (not shown). The ray of reflected light generated on the incident plane 141B causes a loss to the Fresnel lens 141.
The ray of transmitted light Lt1 refracted on the incident plane 141B and transmitted through the total reflection type prism portion 141A reaches the total reflection plane 141C at an angle which is made to the normal m18 and is larger than the critical angle, the ray of transmitted light Lt1 is totally reflected on the total reflection plane 141C, and the ray of transmitted light Lt1 totally reflected is transmitted as the ray of transmitted light Lt2. Because an optical path of the ray of transmitted light Lt1 is bent by using the phenomenon of the total reflection, no ray of light is transmitted through or goes out from the total reflection plane 141C. Therefore, loss in the transmitted light Lt1 is hardly generated on the total reflection plane 141C.
The ray of transmitted light Lt2 totally reflected on the total reflection plane 141C is transmitted at an angle of φ to the normal m16 and reaches the outgoing plane 141D. A part of the ray of transmitted light Lt2 is changed to a ray of reflected light (not shown), and the remaining part of the ray of transmitted light Lt2 is transmitted through the outgoing plane 141D and goes out as a ray of outgoing light Lo at an outgoing angle of “f” (0 degree in FIG. 5A).
Because an optical path is bent in each of the Fresnel lens 121 having the refraction type prism portions 121A and the Fresnel lens 131 having the refraction type prism portions 131A according to the refraction phenomenon, it is required that the ray of incident light Li is received in each of the Fresnel lenses 121 and 131 at a large real incident angle of “a” or “b” to bend the optical path to a considerable degree. Therefore, a ratio of the ray of reflected light Lr to the ray of incident light Li on each of the incident planes 121B and 131B is increased, and the transmissivity of each of the Fresnel lenses 121 and 131 for the ray of incident light Li is undesirably decreased.
In contrast, in the Fresnel lens 141 having the total reflection type prism portions 141A, because the optical path is bent according to the total reflection phenomenon, a degree of the bending of the optical path based on the refraction phenomenon can be reduced. Therefore, the ray of incident light Li can be incident on the incident plane 141B at a small real incident angle of “b”, the increase of the reflectivity of the Fresnel lens 141 can be suppressed, and high transmissivity of the Fresnel lens 141 can be obtained.
As is described above, differently from the Fresnel lenses 121 and 131, high transmissivity can be obtained for the large incident angle in the Fresnel lens 141 having the total reflection type prism portions 141A.
However, as shown in FIG. 5B, in cases where the incident angle of “a” is decreased in the Fresnel lens 141, the ray of incident light Li received on the incident plane 141B is decreased, a ratio of the rays of transmitted light Lt2 totally reflected on the total reflection plane 141C to the rays of incident light Li is decreased, and rays of ineffective light Le (placed in an area of slash marks in FIG. 5B) are inevitably generated.
Though each ray of ineffective light Le is transmitted through the inside of the total reflection type prism portion 141A, the total reflection of the ray of ineffective light Le on the total reflection plane 141C is not performed. Therefore, the rays of ineffective light Le cause a loss to the Fresnel lens 141. In other words, the transmissivity of the Fresnel lens 141 for the rays of incident light Li depends on the incident angle. Therefore, though the transmissivity of the Fresnel lens 141 for the high incident angle of “a” can be heightened, the transmissivity of the Fresnel lens 141 for the low incident angle of “a” is undesirably decreased.
Because each conventional Fresnel lens has the above-described configuration, a problem has arisen that the transmissivity of the conventional Fresnel lens for the rays of incident light Li considerably depends on the incident angle.
Therefore, in each conventional Fresnel lens, a part of image light projected on a screen on a slant at an angle larger than a maximum projection angle cannot be deflected to a desired direction, and the transmissivity of the conventional Fresnel lens for the rays of incident light Li is low.
Here, a conventional Fresnel lens will be briefly described below once more.
FIG. 6 is a view, partially in cross-section, of a conventional Fresnel lens on which image light is projected on a slant.
In FIG. 6, 100 indicates a conventional Fresnel lens in which a plurality of refraction type prism portions are arranged in a plurality of pitch areas. 100a indicates an incident plane disposed on a light incident side of the Fresnel lens 100. 100b indicates an ineffective plane disposed on a light incident side of the Fresnel lens 100. 100c indicates an outgoing plane disposed on a light outgoing side of the Fresnel lens 100. R1in indicates a light flux incident on the incident plane 100a. R2in indicates a light flux incident on the ineffective plane 100b. 
The Fresnel lens 100 shown in FIG. 6 has a plurality of very small refraction type prism portions each of which denotes a unit of prism portion. In each refraction type prism portion, a light flux R1in incident on the incident plane 100a on a slant is deflected and goes out as a light flux R1out through the outgoing plane 100c. 
However, a light flux R2i incident on the ineffective plane 100b different from the incident plane 100a does not go out in a desired direction but goes out as stray light. Therefore, the light flux R2i cannot be effectively used, and the transmissivity of the Fresnel lens 100 is low.
A Fresnel lens having a plurality of total reflection type prism portions is proposed as a means for solving the above-described problem, and rays of light are deflected in the Fresnel lens according to the total reflection.
For example, a Fresnel lens having a plurality of refraction type prism portions and a plurality of total reflection type prism portions alternately disposed is proposed in Published Unexamined Japanese Patent Application No. 52601 of 1986. Also, a Fresnel lens having a plurality of prism portions is proposed in Published Unexamined Japanese Patent Application No. 19837 of 1987, and are fraction using portion and a total reflection using portion are disposed in each prism portion.
However, in the Fresnel lens disclosed in the Published Unexamined Japanese Patent Application No. 52601 of 1986, a refraction type prism portion additionally exists in an area in which the refraction type prism portion does not effectively function, and a total reflection type prism portion additionally exists in an area in which the total reflection type prism portion does not effectively function. Therefore, a problem has arisen that a large amount of light does not still go out in a desired direction.
In contrast, in the Fresnel lens disclosed in the Published Unexamined Japanese Patent Application No. 19837 of 1987, the shape of the Fresnel lens in section is formed in a polygonal shape. Therefore, in cases where a lens forming mold used to form the Fresnel lens is manufactured, a cutting tool having a specific shape is required, and it is difficult to manufacture the lens forming mold. In its turn, it is difficult to manufacture the Fresnel lens.
Also, in cases where each conventional Fresnel lens is applied to a rear projection type screen, a problem has arisen that the brightness of an image displayed on the screen is not uniformly set.
In detail, in cases where a Fresnel lens having refraction type prism portions is applied to the screen, the Fresnel lens cannot effectively function in case of a large projection angle. Therefore, the brightness of an image displayed in a peripheral area of the screen is undesirably lowered, and the thinning of the image displaying device is restricted.
Also, in cases where a Fresnel lens having total reflection type prism portions is applied to the screen, the Fresnel lens cannot effectively function in case of a small projection angle. Therefore, the brightness of an image in an area of the screen placed in the neighborhood of an optical axis is undesirably lowered.
The present invention is provided to solve the above-described problems, and the object of the present invention is to provide a Fresnel lens in which the dependence of transmissivity on an incident angle is lowered.
Also, the present invention is to provide a screen, in which unevenness of the brightness of an image is suppressed in a range from a small projection angle to a large projection angle, and to provide an image displaying device to which the screen is applied.
In addition, the present invention is to provide a lens forming mold manufacturing method, in which a lens forming mold of the Fresnel lens is manufactured, and a lens manufacturing method using the lens forming mold manufacturing method.